Abstract

We consider the conic feasibility problem associated with linear homogeneous systems of inequalities. The complexity of iterative algorithms for solving this problem depends on a condition number. When studying the typical behaviour of algorithms under stochastic input one is therefore naturally led to investigate the fatness of the distribution tails of the random condition number that ensues. We study an unprecedently general class of probability models for the random input matrix and show that the tails decay at algebraic rates with an exponent that naturally emerges when applying a theory of uniform absolute continuity which is also developed in this paper.

Raphael Hauser was supported through grant NAL/00720/G from the Nuffield Foundation and through grant GR/M30975 from the Engineering and Physical Sciences Research Council of the UK. Tobias Müller was partially supported by EPSRC, the Department of Statistics, Bekker-la-Bastide fonds, Dr Hendrik Muller's Vaderlandsch fonds, and Prins Bernhard Cultuurfonds.